Optical path length measurements, made by interferometry, are highly sensitive and adaptable to the study of a wide range of physical phenomena because they sensitively measure small changes in the optical path length induced by physical process, of the order of a fraction of an optical wavelength.
Optical path length variations may be induced in the distance between a point on the surface of an object and the corresponding point on the image plane formed by an imaging system used to make an image of the object in the presence of externally applied perturbations. A number of physical and chemical phenomena provide mechanisms for inducing spatial distribution in such changes of the optical path length that may then be interferometrically probed. Such mechanisms could include thermal or electromagnetic excitation, or acoustic or mechanical perturbation of the material, or chemically modifying the object's surface. When interferometry is used to record images of such objects, it may provide a method of imaging the physical process that induces the optical path length change. Because of the many physical and chemical phenomena which are capable of producing optical length changes, which interferometry may potentially probe with very high optical length resolution, imaging methods based on interferometry have widespread applications in industrial measurement.
When a material sample is subjected to a perturbation, any resulting changes in the optical path length to the image plane may be potentially sensed by an interferometer. Optical path length variations occurring along the transverse coordinate of the interferometer may be probed to form an interferometric image: the transverse coordinates of the interferometer are defined as occupying orthogonal directions, (x,y) that lie in the image plane. The primary interferometric image produced by the interferometer is called an interferogram. The interferogram is defined as an image formed by the superposition of two beams of coherent light, I1 and I2, on the image plane of the interferometric imaging system. The interferogram is electronically recorded (such as by a camera considered to be a generalized imaging device composed of an array of optical sensing elements (or image pixels) operating over the wavelength range used by the interferometer beams) and the information is stored in a data storing and processing system. The interferogram is commonly referred to as a speckle image when a coherent light source is used and the object's surface roughness causes random reflection forming speckles on the image plane. When multiple images are taken, for instance of an object in various stages of deformation, each speckle image is considered a frame.
In speckle pattern interferometry, a speckle pattern image of the object before modification or perturbation (henceforth considered as a “deformation”) is electronically stored. Next a speckle pattern image of the object after deformation is electronically stored. By taking the difference between the speckle pattern images before and after deformation it is possible to observe a speckle interference fringe pattern. The interference pattern appears as dark and light regions which show the deformation distribution.
General equipment for creating interferometric images is shown in FIGS. 1 and 2. The apparatus generally consist of:                a) a coherent radiation source, such as a laser, the radiation source emits a source beam having a spatial coherence length;        b) a beam splitter at which the source beam is separated (by partial reflection or other means) into one (or more) beam(s). In “in-plane” interferometry, the source beam is split into two probe beams I1 and I2. Each probe beam illuminates the object, but are separated by an angle alpha. In-plane interferometry is sensitive to in-plane displacements. In “out-of-plane” interferometry, the source beam is split into a probe beam I1 which illuminates the object and a reference beam I2 which is phase coherent with the probe beam and which combines with the illumination beam after interaction with the object. Out-of-plane interferometry is sensitive to out-of-plane displacements.        c) a test medium positioned to be intersected by the probe beam(s) and reflect the incident radiation, and        d) an image plane or surface in which the reflected probe(s) and reference beam are superimposed so as to produce electromagnetic wave interference, thus forming an image of the object.        
The system may include lenses, mirrors or other beam directing elements to accomplish the beam splitting. In making a measurement, the intensity (the squared amplitude of the interfered waves from the two beam lines) is recorded by the charged coupled camera device or similar device. Hence, it is desirable to recover the phase information from the amplitude information recorded. Several methods have been proposed, most require shifting the relative phase of the probe beams in known amount. All such methods are computationally burdensome. In addition, they require multiple images be taken, therefore are not applicable to applications where the deformation is continuous because the phase change to be evaluated varies when the extra images are taken.